WEEK 7 - Portfolio Analysis (NOT YET COMPLETE)

Question 1

How do we calculate the expected return on a two asset portfolio?

Answer 1

R(bar)P = WaRa +WbRb

Where:
R(bar)p = Expected return on Portfolio 
Ra = Return on Security A
Rb = Return on Security B
Wa = Share of Security A in portfolio
Wb = Share of Security B in portfolio

Question 2

How do you calculate the standard deviation of a two asset portfolio?

Answer 2

σp = Square root of (W2Aσ 2A + w2B σ 2B + 2WaWb COV (RA,RB)

Where:
σp  = Portfolio Standard Deviation
σA2= Variance of Investment A
σB2 = Variance of Investment B 
COV(Ra,Rb) = Covariance of A and B

SEE EXAMPLE IN NOTES

Question 3

How do we calculate the Covariance of A and B?

Answer 3

COV(Ra,Rb) = SIGMA (Ra - R (bar)a) (Rb - R(bar)b)pi

Where:
R(bar)a = Expected Return on A
R(bar)B = Expected Return on B

SEE EXAMPLE IN NOTES

Question 4

How do we calculate the correlation coefficient?

Answer 4

P a,b = COV (Ra,Rb) / σa σb

SEE EXAMPLE IN NOTES

Question 5

What is the correlation scale?

Answer 5

Ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related (Negatively or Positively). If r is close to 0, it means there is no relationship between the variables.

Question 6

What does the degree of risk reduction depend on?

Answer 6

the extent of statistical interdependence between the returns of the different investments

the number of securities over which to spread the risk

Question 7

What is the general rule in portfolio theory?

Answer 7

Portfolio returns are a weighted average of the expected returns on the individual investment . . .

BUT . . .

Portfolio standard deviation is less than the weighted average risk of the individual investments, except for perfectly positively correlated investments.

Question 8

How can we rewrite the Standard Deviation considering we know about the Covariance?

Answer 8

Since we know the COV of A and B

Can rewrite St.Dev as (CHECK NOTES)

Question 9

What is the Efficient Frontier for Portfolio Analysis?

Answer 9

Set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.

(SEE GRAPH IN NOTES)

Question 10

What is the Indifference Curve for Portfolio Analysis?

Answer 10

Describe investor demand for portfolios based on the trade-off between expected return and risk.
It is a convex curve, meaning upward curving and where it meets the Efficient Frontier there is a match between supply and demand. This spot is called the Optimal Portfolio.

Question 11

How are the varying degrees of risk displayed in the Indifference Curve?`

Answer 11

SEE IN NOTES

Question 12

How do you plot the points of a two asset model where both assets are perfectly correlated?

Answer 12

It is only possible to create along a straight line between the 2 assets

SEE GRAPH IN NOTES

Question 13

How do you plot the points of a two asset model where both assets are uncorrelated? (+0.00)

Answer 13

Only possible to create a two asset portfolio with risk return along a line between either asset.

SEE GRAPH IN NOTES

Question 14

How do you plot the points of a two asset model where both assets are correlated? (+0.5)

Answer 14

Only possible to create a two asset portfolio between the first two curves

SEE GRAPH IN NOTES

Question 15

How do you plot the points of a two asset model where both assets are negatively correlated? (-0.5)

Answer 15

Possible to create a two asset portfolio with much lower risk than either asset

SEE GRAPH IN NOTES

Question 16

How do you plot the points of a two asset model where both assets are perfectly negative correlated? (-1.0)

Answer 16

Possible to create a two asset portfolio with almost no risk

SEE GRAPH IN NOTES

Question 17

What does a three asset portfolio look like?

Answer 17

SEE GRAPH IN NOTES

Question 18

What does a Multi-Security Portfolio look like?

Answer 18

SEE GRAPH IN NOTES

Question 19

How can we identify if something is or isn’t a diversifiable risk or a Non-diversifiable risk?

Answer 19

SEE GRAPH IN NOTES

Question 20

What are the benefits of International Diversification?

Answer 20

International shares may provide a lower risk as a percentage of the risk on a single share

Question 21

What does the Capital Market Line look like as a Portfolio?

Answer 21

SEE GRAPH IN NOTES

Question 22

What does the Capital Market Line look like as a Portfolio with indifference curves attached?

Answer 22

SEE GRAPH IN NOTES

Question 23

What are the problems with Portfolio theory?

Answer 23

• Implemented using historic returns- Standard deviations and correlations to aid decision making about future investment
• The volume of Computations for large portfolios can be inhibiting
• The accurate estimation of indifference curves is an elusive goal